Having pretty much seen it and done it all in a sport where, he believes, nobody is too old to learn or improve, Novak Djokovic still has some progress to make, even in his already storied career.

His physicality at the age of 38? Perhaps. His mental freshness to keep going with 24 majors under his belt? Maybe. His mastery of foreign languages? Of course.

The Serbian great made it obvious at the ongoing Rolex Shanghai Masters that he's become better at presenting his post-match homework in the East China metropolis, as he barely missed a stroke while writing his name in Chinese on the lens of the TV camera following his latest win on Sunday.

The four-time winner in Shanghai also proved he's better at fighting under brutally hot and humid conditions, overcoming a first-set scare to beat German ace Yannick Hanfmann 2-1 to reach the fourth round at the season's penultimate ATP 1000 tournament.

As proud as he is of handling the on-court challenge, Djokovic took more satisfaction from knowing that his effort to appreciate his unrivaled fan support in China was well received.

"A little bit. A little bit," Djokovic said with a grin in the mixed zone, after being asked if he had been practicing his Chinese handwriting.

"The fans showed me (how to make it right)," said Djokovic, who, on Friday, had to take a long pause, trying to remember the strokes, while writing the same, fairly complicated Chinese character following his first match.

I have to go through my characters. I knew quite a few of them, but I have lost them somewhere, and I haven't been really working on them, so I have to update my Chinese knowledge.

"It's always a pleasure to play in front of such passionate fans. People have been giving me lots of love and support over the years, so I try to give back to them with good tennis, and also a basic knowledge of the Chinese language with a few phrases."

A crowd favorite in China, where he holds the record for most titles at both the Shanghai Masters and the ATP 500 China Open in Beijing (six), said the reunion with his Chinese fans was the main reason he'd decided to return to Shanghai and compete at an event few would have expected him to attend so close to the end of the season.

After all, pursuing a record-breaking 25th major singles trophy seems to be the only unfinished on-court business for the man who already holds multiple all-time records, including the most number of weeks at world No 1 (428), the most titles at the ATP 1000 level (40) and the most ATP Finals wins (seven).

The key to the celebrated veteran's longevity was laid bare on Sunday, when he dug deep to pull through a tough night, while his younger rival Jannik Sinner, one of the biggest obstacles to the Serb's hunt for his elusive 25th major, had to retire from his own third-round match in Shanghai, due to a serious cramp in his right thigh.

The 24-year-old Italian world No 2 was forced to stop midway through the deciding set against Tallon Griekspoor, with the cramp growing too painful to withstand.

Djokovic also had to battle against his own discomfort, which saw him vomit during a changeover, while hitting against the big-serving Hanfmann at the packed Stadium Court.

The German qualifier's booming serve and variety of drop shots did quite a bit of damage in the first set, threatening to derail Djokovic's bid for a fifth Shanghai title, before the Serb intentionally shortened the rallies with more precision to regain control and pull off a 4-6, 7-5, 6-3 win in two hours and 45 minutes — his second-longest best-of-three battle in 2025.

The vocal support from his local "Nole-Fam" provided a much-needed boost for the current world No 5.

"I am proud to overcome the big challenge, and I want to thank the Chinese for supporting me tonight, their energy was amazing," said Djokovic, who will meet Spain's No 41 Jaume Munar in the fourth round on Tuesday.

"Their support is something that motivated me to come this year and play in Shanghai.

"These first two matches are testament to how welcome I feel in China in general, and Shanghai specifically, so I am very grateful and blessed to be able to experience an atmosphere like tonight."

Since his arrival early last week, every one of Djokovic's public appearances, either at his hotel entrance or on the practice courts at the Qizhong Tennis Center, has been swarmed by fervent fans, so much so, that security was drafted in to help him make his way in and out.

He also tries not to disappoint those fans, each time, signing as many autographs as his tight schedule will allow and taking as many selfies with them as possible.

"It's stunning, honestly, I cannot ask for more. I'm grinding for almost three hours, third round of a Masters at 38 with the full stadium cheering my name. It's a dream come true for me, so I'm very thankful," said Djokovic, who's racked up 41 wins, the most among anyone, across his 11 appearances at the Shanghai event.

Djokovic will take a 1-0 head-to-head lead into Tuesday's clash with Munar, who earlier fought past Japan's Yoshihito Nishioka 6-4, 5-7,6-1 to reach this stage of a hard-court ATP Masters 1000 tournament for the first time in his career.

sunxiaochen@chinadaily.com.cn